Why am I getting UV distortion on a flat surface?
To get a nearly undistorted UV, the modeling topology should be made by even quads, with every pole made only of 4 edges (5 and 3 where strictly necessary), which is not your case. Anyway, as the surface is flat, you can set the 3D view in a front ortographic perspective, select all the faces of the flat surface and press U "Project from view" and you will get an undistorted UV. Then you can select all the UV islands in the UV editor and average and pack everything.